

Title of Thesis
Relationship Between Mathematical Thinking And Achievements In
Mathematics Among Secondary School Students Of Nwfp Pakistan 
Author(s)
Amir Zaman 
Institute/University/Department
Details Department Of Education, Faculty Of Social
Sciences / International Islamic University, Islamabad 
Session 2011 
Subject Education 
Number of Pages 311 
Keywords (Extracted from title, table of contents and
abstract of thesis) Mathematical, Grade, Relationship,
Relation, Teachers, Quantitative, Achievements, Secondary, Analysis,
School, Investigate, Perceptions, Interviews 
Abstract
This study aimed to investigate the relationships between mathematical thinking
and achievement in mathematics in the 9th grade scientific stream students in North West
Frontier Province, Pakistan which was renamed as Khyber Pakhtunkhwa by the
parliament of Pakistan through 18th constitutional amendment in 2009.In addition, this
study also investigated the gender, school sector, and school location differences in
mathematical thinking and mathematics achievement.Besides, this study also
investigated the interaction between gender and school location, gender and sector, sector
and location, in relation to mathematical thinking and achievement.
Further, this study examined conceptions of teachers about mathematical thinking
and any inconsistencies between the teachers’ opinions about the aspects of mathematical
thinking in terms of level of importance, level of difficulty and the results derived from
the quantitative analyses of the student answers to the mathematical thinking test.
In relation to the student interviews, the study also aimed to identify popular
strategies used by students to arrive at solutions, question understanding, their
perceptions about difficulty level of aspects of mathematical thinking and to differentiate
between the thinking skills they used and to ascertain their attitude towards optimal
solutions like checking their solutions.
To achieve the above mentioned objectives, a model of mathematical thinking
was first developed representing the best possible six aspects of mathematical thinking
relevant to the curriculum of grade 9 in Pakistan with the help of experts and practising
teachers.A test of mathematical thinking was developed based on this model to measure
mathematical thinking of the students.Besides a test of mathematics achievement with
items taken from textbook of grade 9 and two interviews (one for teachers and one for
students) were also conducted for data collection.Quantitative data was analyzed using
ttest, Anova and regression analysis.Similarly qualitative data from interviews was
analyzed using qualitative data analysis techniques.Main findings of the study showed
that mathematical thinking was moderately related to mathematics achievement with
proofs as the most correlated aspect.The study further showed that male students
outperformed their female counterparts. In the same way, the students of the private
schools scored significantly better than the students of public schools in all aspects of
mathematical thinking and mathematics achievement.
Teachers’ interview revealed that problem solving, induction, deduction, logical
thinking, proofs and optimal solution were the most important aspects of mathematical
thinking with proofs as the most difficult and generalization as the easiest aspects.Teachers expressed their opinions that studentcentered teaching was the effective way in
teaching of mathematics.

